Nope. I've had safe deposit boxes in a number of institutions and they all required use of two keys to access - one held by the customer (me) and the other by the bank. I go in, sign a card/fill out a form that records who accessed it when (one bank always checked my photo ID, others took my word that I was who I claimed to be), sometimes had the signature compared to the one on file, put my key in one lock and they put their key in the other. Even though in theory the paperwork specified who had access to the box, the fine print covered their butts with wording to the effect that "anyone possessing the key is assumed to be authorized to access the box contents", and the ID/signature-check just to make sure it's not someone pretending to be *me*.
The signup and disclosure forms made a huge deal out of making sure I knew I had to bring my key every time, they couldn't do it with just their key, and "don't lose your key, we can't open the box. You have to fill out paperwork and pay us in advance a fee to cover both drilling the lock and then replacing it and issuing new keys because that's going to destroy it".
Now what would be interesting is how the bank handles this without the backup paperwork ... who/what has the backup copy of the records of who's got what box number, the cards with accountholder info and alternate accesses and access history and so on. My previous bank went from small-local to itty-bitty-branch-of-huge-one to bankrupt-huge-one-gets-bought-by-even-bigger-one, yet the original account open cards, signatures, info, etc, were always in the same beat-up old box in an office that wasn't inside the vault. If this branch had been in Joplin, those records would be in a field a few dozen miles away.
Things are quite different with safe deposit boxes vs stuff left at a hotel office, for example.
Anyhow, sorry to digress so much. Business continuity after disaster is sort of an interest of mine.